Thesis Committee: Professors Deepto Chakrabarty (Chair), Claude Canizares & Nevin Weinberg
X-ray binaries are test beds for studies of high-energy accretion flows and the properties of compact objects. Accreting neutron stars in low-mass X-ray binaries vary in brightness by almost 8 orders of magnitude and are hosts to diverse accretion flows, transporting varying amounts of energy and mass toward the central neutron star, as well as expelling significant mass from the binary. This thesis studies the accretion flow properties across the luminosity scale with particular emphasis on constraining the matter accreted onto the neutron star surface and the resulting heating, which has important implications for measurements of the neutron star mass and radius. We have utilized X-ray instruments with substantially different sensitivities in flux and resolving power, each suited to our focused study of the accretion flows in a particular luminosity regime. Our findings include the detection of the cooling neutron star in a faint quiescent low-mass X-ray binary, as well as a potential accretion hotspot on the surface of another accreting neutron star in quiescence. The former result is in agreement with standard theories of neutron star heating and cooling, while the latter heralds new evidence for neutron star heating in quiescence.